I have awarded Heroes of Might & Magic III Complete a Gold Medal, because the game installs and works great on the Mac Platform under Crossover Games 9.0.
At the same time, there is care to be taken. I have found that after extensive playing, there are rare crashes of the program--crashes that are fatal to the game. Whether for good or ill, I cannot recreate these crashes at will and even when there is a crash, I can go back and do the exact same things without any crash whatsoever. This leads me to believe that it is an instability in Wine or Crossover itself, not a problem from this game.
Out of fairness, I must say that I can play hours without any problems; so this really is a rare thing. Just be careful. Save often, so as to not lose your progress.
Edit by Kivanc Muslu: I agree to Jason as I have also encountered some fatal errors during gameplay. Autosave in the game (default) is your savior :)